Thermal radiation from nonisothermal spherical particles of a semitransparent material Leonid A. Dombrovsky Heat Transfer Department, Institute for High Temperatures of the Russian Academy of Sciences, Krasnokazarmennaya 17A, Moscow 111250, Russia Abstract The applicability of radiation transfer theory for calculations of the thermal radiation emitted by spherical particle of a semitransparent material, and in particular the determination of radial heat generation pro®les, is analyzed. For homogeneous isothermal particles, a comparison with the exact solution based on the Mie theory shows that the radiation transfer calculations are suciently accurate for diraction parameter of the particle of xr 20. Numerical examples for large particles illustrate the transition from conditions of dominant radiation of the central region of the particle to conditions of the surface layer emission. A new dierential approximation for radiation transfer in a refracting particle is proposed. This approximation called MDP 0 (modi®ed DP 0 ) is much simpler than the radiation transfer equation. Using MDP 0 , we have a chance to consider radiation±conduction interaction in nonisothermal particles without great computational eorts. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Heat; Radiation; Emission; Particle; Oxide 1. Introduction In analyzing radiation heat transfer in disperse systems containing particles up to hundreds of microns in size, a single particle is usually considered to be isothermal. This assumption greatly simpli®es the calculation of the thermal radiation of the par- ticle. At the same time, in the case of intensive cool- ing, the temperature dierence between the center and the surface of the particle may be considerable. One example is the problem of vapor explosion in a nuclear reactor severe accident due to thermal inter- action of molten uranium oxide droplets having initial temperature of about 3200 K with ambient boiling water [1]. Thermal radiation of a nonisothermal particle is an especially interesting problem for particles of a semi- transparent material (in particular, for metal oxide particles). The point is that materials, which are semi- transparent in the infrared spectral range, are usually characterized by low thermal conductivity and, as a result, by a comparatively large temperature dierence between the center and the surface of the particle. On the other hand, in the case of a small index of absorp- tion, the solution to the problem is expected to be more complex because of the possible considerable contribution of radiation emitted from the central high-temperature core of the particle. A rigorous statement of the problem must take into account eects of interference as is done in the Mie theory. At the same time, in the case of large particles, for which the temperature dierence is International Journal of Heat and Mass Transfer 43 (2000) 1661±1672 0017-9310/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII:S0017-9310(99)00231-8 www.elsevier.com/locate/ijhmt